Light-cone effect and clustering of high-z objects

While all the cosmological observations are carried out on the null hypersurface of an observer at z = 0, or, the light-cone, the clustering statistics has been properly defined only on the constant-time hypersurface. We develop a theoretical formulation for the two-point correlation functions on the light-cone, and derive the practical approximate expressions relevant to the discussion of clustering of high-redshift objects at large separations. As a specific example, we present predictions of the two-point correlation functions for the Durham/AAT, SDSS and 2dF quasar catalogues. We also briefly discuss the effects of adopted luminosity function, cosmological parameters and bias models.